Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 2 / 6E / b / Solution

Let $J_{+}=\lambda$ and $J_{-}=2\beta m^2$ be the production and loss fluxes, counted in molecules per unit time. At the steady state, both equal $J=\lambda$. The restoring elasticity and turnover lifetime areFlux-weighting the magnitudes of the reaction steps, one for production and two for loss, givesThis is an average over molecular fluxes, as requested, not an average over reaction-event counts; those are different when a reaction removes two molecules at once.